ReportClaimsAppleIsTesting12.9-InchiPadsWith2K,4KDisplays

One recent report claims that Apple's go-to assembler, Foxconn, has built several prototype units of a 12.9-inch iPad, each of which features either a 2K or 4K ultra-high resolution display. Though the article, from PadNews, doesn't outright confirm that a 12.9-inch iPad is in the cards, it does speculate that a bigger, higher resolution model could launch as soon as 2014.
More specifically, the Chinese language publication speculates that the 2K display-equipped 12.9-inch iPad could launch in the first half of 2014, and that the 4K display-equipped model might launch in the following months, later in 2014.
Given that Apple rebranded its 9.7-inch iPad as the "iPad Air" earlier this year, analysts have anticipated that an "iPad Pro" could be released (à la MacBook) at some point in the future.
Of course, there's also been no shortage of reports claiming that a larger iPad, be it the iPad Pro or "iPad maxi," is in the cards for either 2014 or 2015. These go as far back as May this year, before an iPad Air had even been announced; a few months later a convincing mockup showed how a 12.9-inch iPad might look (pictured above), and following this a lengthy article from DisplaySearch analyst and vice president David Hsieh claimed that a 12.9-inch iPad is indeed set to launch in 2014:

Hsieh also argues that a 12.9-inch iPad featuring a resolution of 2,732 by 2,048 is in the works, and will launch at some point in 2014. Indeed, this isn’t unfamiliar news, either.

It's perhaps worth noting, in retrospect, that Hsieh's predictions concerning the iPad mini with Retina display were indeed correct, despite being published during a period when most analysts were arguing that "supply concerns" could see the high resolution 7.9-inch tablet get postponed.
Following on from here, KGI Securities analyst Ming-Chi Kuo argued that an iPad with a 30-40 percent higher pixel density could launch next year, and several other reports have corroborated on this front.
The actual resolution of Apple's anticipated 12.9-inch iPad's 2K and 4K displays is a point of debate, too. Unwired View correctly notes that in actual fact, "the 2,048×1,536 resolution already employed by Apple in its latest full size iPads could be '2K' itself," since such displays are defined by their horizontal resolutions of 2,000 pixels.
The publication adds:

As for '4K,' that’s going to have around 4,000 pixels per each line. If Apple keeps the aspect ratio 4:3 (and it’s never changed it in tablets ever since the first iPad came out, so there’s no reason not to), then its flavor of '4K' will most likely be 4,096×3,072.